Non-reductive Homogeneous Pseudo-Riemannian Manifolds of Dimension Four
By M. Fels, A. Renner. Canadian Journal of Mathematics - Journal Canadien de Mathematiques, 2004
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Abstract A method, due to Élie Cartan, is used to give an algebraic classification of the non-reductive homogeneous pseudo-Riemannian manifolds of dimension four. Only one case with Lorentz signature can be Einstein without having constant curvature, and two cases with (2, 2) signature are Einstein of which one is Ricci-flat. If a four-dimensional non-reductive homogeneous pseudo-Riemannian manifold is simply connected, then it is shown to be diffeomorphic to ${{\mathbb{R}}^{4}}$ . All metrics for the simply connected non-reductive Einstein spaces are given explicitly. There are no non-reductive pseudo-Riemannian homogeneous spaces of dimension two and none of dimension three with connected isotropy subgroup.
Subfields: Applied Mathematics, Astronomy and Astrophysics, Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/99b26814eadb8b0ff337a9d1241855b899420a31
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Citations in the corpus
- Ricci Solitons and Geometry of Four-dimensional Non-reductive Homogeneous Spaces (2012, background): “In the basic paper [14], the classification of four-dimensional, nonreductive, homogeneous, pseudo-Riemannian manifolds was obtained, showing the Received by the editors January 26, 2011.”